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arXiv · 2101.00889

Background construction for $λ$-indexed mice

Farmer Schlutzenberg
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Abstract

Let $M$ be a $λ$-indexed (that is, Jensen indexed) premouse. We prove that $M$ is iterable with respect to standard $λ$-iteration rules iff $M$ is iterable with respect to a natural version of Mitchell-Steel iteration rules. Using this equivalence, we describe a background construction for $λ$-indexed mice, analogous to traditional background constructions for Mitchell-Steel indexed mice, and which absorbs Woodin cardinals from the background universe. We also prove some facts regarding the correspondence between standard iteration trees and u-iteration trees on premice with Mitchell-Steel indexing.

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Farmer Schlutzenberg. 2021-01-09. Background construction for $λ$-indexed mice. https://arxiv.org/abs/2101.00889

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